Q.In a reaction $A + B_2 \rightarrow AB_2$ identify the limiting reagent, if any, in the following reaction mixtures.

The key idea here is Limiting Reagent Identification.

A limiting reagent is the reactant that is completely consumed first in a chemical reaction, thereby determining the maximum amount of product that can be formed. To identify it, we compare the available amounts of reactants to their stoichiometric ratio from the balanced chemical equation.

The given reaction is $A + B_2 \rightarrow AB_2$.

From the balanced equation, 1 unit (atom or mole) of A reacts with 1 unit (molecule or mole) of $B_2$. The stoichiometric ratio of A to $B_2$ is $1:1$.

We will analyze each mixture:

(i) 300 atoms of A + 200 molecules of B

• We have 300 atoms of A and 200 molecules of $B_2$.
• Since the reaction ratio is $1:1$, 200 molecules of $B_2$ would react completely with 200 atoms of A. …

When chemicals react, they do so in specific proportions dictated by the balanced chemical equation. Imagine you are building bicycles. If each bicycle needs 1 frame and 2 wheels, and you have 10 frames and 15 wheels, you can only build 7 bicycles (because 15 wheels / 2 wheels per bicycle = 7.5, but you can't have half a bicycle, and you only have 10 frames). The wheels run out first, limiting the number of bicycles you can make. In chemistry, the reactant that gets completely used up first, thus stopping the reaction and limiting the amount of product formed, is called the limiting reagent (or limiting reactant).

To identify the limiting reagent, we need to:

1. Understand the stoichiometry: Determine the mole (or atom/molecule) ratio in which the reactants combine, based on the balanced chemical equation.
2. Compare available amounts: See how the actual amounts of reactants provided compare to this stoichiometric ratio. The reactant that is present in a smaller proportion than required by stoichiometry will be the limiting reagent.

The given reaction is:

$A + B_2 \rightarrow AB_2$

From this balanced equation, we can see that:

• 1 atom of A reacts with 1 molecule of $B_2$.
• 1 mole of A reacts with 1 mole of $B_2$.

This means the stoichiometric ratio of A to $B_2$ is $1:1$. For every unit of A, we need one unit of $B_2$.

Let's apply this understanding to each reaction mixture.

(i) 300 atoms of A + 200 molecules of B

1. Identify given quantities: We have 300 atoms of A and 200 molecules of $B_2$.
2. Determine stoichiometric requirement: According to the balanced equation, 1 atom of A reacts with 1 molecule of $B_2$.
3. Compare available amounts to stoichiometry:
   • If all 200 molecules of $B_2$ were to react, they would require 200 atoms of A.
   • We have 300 atoms of A, which is more than the 200 atoms required.
   • This means $B_2$ will be completely consumed before A runs out.
   • Alternatively, if all 300 atoms of A were to react, they would require 300 molecules of $B_2$. We only have 200 molecules of $B_2$, which is less than required.
4. Conclusion: $B_2$ is the limiting reagent.

(ii) 2 mol A + 3 mol B

1. Identify given quantities: We have 2 mol of A and 3 mol of $B_2$.
2. Determine stoichiometric requirement: According to the balanced equation, 1 mol of A reacts with 1 mol of $B_2$.
3. Compare available amounts to stoichiometry:
   • If all 2 mol of A were to react, they would require 2 mol of $B_2$.
   • We have 3 mol of $B_2$, which is more than the 2 mol required.
   • This means A will be completely consumed before $B_2$ runs out.
   • Alternatively, if all 3 mol of $B_2$ were to react, they would require 3 mol of A. We only have 2 mol of A, which is less than required.
4. Conclusion: A is the limiting reagent.

(iii) 100 atoms of A + 100 molecules of B

1. Identify given quantities: We have 100 atoms of A and 100 molecules of $B_2$.
2. Determine stoichiometric requirement: According to the balanced equation, 1 atom of A reacts with 1 molecule of $B_2$.
3. Compare available amounts to stoichiometry:
   • The available ratio of A to $B_2$ is $100:100$, which simplifies to $1:1$.
   • This exactly matches the stoichiometric ratio of $1:1$.
   • Both reactants will be consumed completely at the same time. …

Method: Limiting Reagent Identification via Stoichiometric Ratio Comparison

This method uses the mole ratio from the balanced equation to determine which reactant runs out first.

Balanced Equation

Stoichiometric ratio:

1 atom of A reacts with 1 molecule of $B_2$ (since $B_2$ provides 2 B atoms, and $AB_2$ needs 2 B atoms per A atom).

So the required ratio is:

Steps

1. Convert all given quantities to moles (if not already in moles).

   • Atoms/molecules → moles: divide by Avogadro’s number ($6.022 \times 10^{23}$).
   • For comparison, you can also directly compare atom/molecule counts since the ratio is 1:1.

2. Find the actual mole ratio:

3. Compare with required ratio (1:1):
   • If actual ratio > 1: A is in excess → $B_2$ is limiting.
   • If actual ratio < 1: $B_2$ is in excess → A is limiting.
   • If actual ratio = 1: No limiting reagent (both are stoichiometric).

Applying to Each Case

(i) 300 atoms of A + 200 molecules of B

• A = 300 atoms, $B_2$ = 200 molecules
• Ratio = $300/200 = 1.5 > 1$
• $B_2$ is limiting

(ii) 2 mol A + 3 mol B

• A = 2 mol, $B_2$ = 3 mol
• Ratio = $2/3 \approx 0.67 < 1$
• A is limiting

(iii) 100 atoms of A + 100 molecules of B

• Ratio = $100/100 = 1$
• No limiting reagent (both exactly match)

(iv) 5 mol A + 2.5 mol B

• Ratio = $5/2.5 = 2 > 1$ …

Here are the common mistakes students make when solving limiting reagent problems like the one given, along with how to avoid each.

Mistake 1: Confusing atoms/molecules with moles

The error:

In parts (i) and (iii), students treat “300 atoms of A” and “200 molecules of B” as if they were moles. They then compare 300 and 200 directly, forgetting that the reaction uses 1 atom of A with 1 molecule of B₂ (since $B_2$ contains 2 B atoms, but the molecule count matters here).

How to avoid:

• Read the reaction carefully:

• The stoichiometric ratio is 1 atom of A : 1 molecule of B₂.
• For (i):
  • 300 atoms of A need 300 molecules of B₂.
  • Only 200 molecules of B₂ are available → B₂ is limiting.
• For (iii):
  • 100 atoms of A need 100 molecules of B₂.
  • Exactly 100 molecules of B₂ are available → no limiting reagent (both are exactly consumed).

Mistake 2: Using the wrong stoichiometric ratio

The error:

Students think the ratio is 1 A : 2 B (because $B_2$ has two B atoms). They then compare moles of A with moles of B atoms instead of moles of B₂ molecules.

How to avoid:

• The balanced equation is:

• The coefficient of $B_2$ is 1, not 2.
• Always use the molecule/mole ratio from the balanced equation, not the atomic count.

Mistake 3: Forgetting to convert “molecules” to “moles” when needed

The error:

In parts (ii), (iv), and (v), quantities are given in moles — no conversion needed. But in (i) and (iii), students sometimes try to convert atoms/molecules to moles unnecessarily and then get confused.

How to avoid:

• For atoms and molecules, you can compare directly using the particle ratio from the equation (since 1 atom : 1 molecule).
• Only convert to moles if the problem asks for mass or volume. Here, the question only asks for the limiting reagent — so particle counts are fine.

Mistake 4: Not checking both reactants — assuming the smaller number is always limiting

The error:

In (ii): 2 mol A + 3 mol B. Students see 2 < 3 and say A is limiting — but the ratio is 1:1, so 2 mol A needs 2 mol B₂. Since 3 mol B₂ is available, A is indeed limiting — but the reasoning must be based on the required amount, not just the raw numbers.

How to avoid:

• For each reactant, calculate how much of the other is needed.
• The limiting reagent is the one that runs out first when you follow the stoichiometric ratio.

Mistake 5: Misidentifying limiting reagent when both are in excess

The error:

In (iv): 5 mol A + 2.5 mol B. Students sometimes say “both are in excess” or pick the wrong one.

How to avoid:

• Ratio required: 1 A : 1 B₂ …